# An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion

arXiv: https://arxiv.org/abs/2008.10532 · HTML: https://mlsanity.com/paper/2008.10532/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2020.

## Built on by (most cited first, 19 of 19)

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- [Solving the Discretised Neutron Diffusion Equations using Neural Networks](https://mlsanity.com/paper/2301.09939/) (2023)
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- [An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes](https://mlsanity.com/paper/2202.06170/) (2022)
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- [Surrogate models for Rock-Fluid Interaction: A Grid-Size-Invariant Approach](https://mlsanity.com/paper/2602.22188/) (2026)

## Abstract (arXiv)

Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional space in which a high-dimensional system is approximated. Proper orthogonal decomposition (POD) and singular value decomposition (SVD) are often used for this purpose and yield an optimal linear subspace. Autoencoders provide a nonlinear alternative to POD/SVD, that may capture, more efficiently, features or patterns in the high-fidelity model results. Reduced-order models based on an autoencoder and a novel hybrid SVD-autoencoder are developed. These methods are compared with the standard POD-Galerkin approach and are applied to two test cases taken from the field of nuclear reactor physics.